Accurate finite element (FE) models are needed in many applications of Civil Engineering such as health monitoring, damage detection, structural control, structural evaluation and assessment. Model accuracy depends on both the model structure (the form of the equations) and the model parameters (the coefficients of the equations), and can be generally improved through that process of experimental reconciliation known as model updating. However, modelling errors, including (i) errors in the model structure and (ii) errors in parameters excluded from adjustment, may bias the solution, leading to an updated model which replicates measurements but lacks physical meaning. In this paper, an application of ambient-vibration-based model updating to a large-scale benchmark prototype of a building structure is reported in which both types of error are met. The error in the model structure, originating from unmodelled secondary structural elements unexpectedly working as resonant appendages, is faced through a reduction of the experimental modal model. The error in the model parameters, due to the inevitable constraints imposed on parameters to avoid ill-conditioning and under-determinacy, is faced through a multi-model parameterization approach consisting in the generation and solution of a multitude of models, each characterized by a different set of updating parameters. Results show that modelling errors may significantly impair updating even in the case of seemingly simple systems and that multi-model reasoning, supported by physical insight, may effectively improve the accuracy and robustness of calibration.